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If the argument of (z-a)(barz-b) is equa...

If the argument of `(z-a)(barz-b)` is equal to that of `((sqrt(3)+i)(1+sqrt(3)i))/( 1+i)` , where a,b are two real numbers and `barz` is the complex conjugate of the Argand diagram. Find the values of a and b so that be locus becomes a circle having its centre at `(1)/(2)(3+i)`.

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Verified by Experts

The correct Answer is:
`x^(2)+y^(2)-(a+b )x-(a-b)y+ab; ab=0;`
`a=2 and b=1`
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